An Algorithm for Alignment-free Sequence Comparison using Logical Match
Sanil Shanker KP Elizabeth Sherly Department of Computer Science Indian Institute of Information University of Kerala , India Technology Management- Kerala e-mail:
[email protected] India . e-mail:
[email protected]
Jim Austin Department of Computer Science University of York, UK e-mail:
[email protected]
Abstract: This paper proposes an algorithm for alignmentfree sequence comparison using Logical Match. Here, we compute the score using fuzzy membership values which generate automatically from the number of matches and mismatches. We demonstrate the method with both the artificial and real datum. The results show the uniqueness of the proposed method by analyzing DNA sequences taken from NCBI databank with a novel computational time.
match logically the indices of the pattern with those of the text. This paper presents the method for alignment-free comparison of sequential patterns of finite length using automatically generating fuzzy membership values by Logical Match[6,7,8,9].
Key words: Alignment-free sequence comparison, Fuzzy membership, Logical Match, String match
The sequence pattern is arranged so that each characters are encoded as binary digits and coincide with the corresponding index and then proceed to match logically the indices of the pattern with those of the text. The algorithm has two phases. The characters in the sequence pattern are pre- processed in the phase- I. The information from the phase- 1 is used in the phase- II in order to reduce the total number of character comparisons. We compute the score using fuzzy membership values which generate automatically from the number of matches and mismatches.
I
INTRODUCTION
Alignment-free sequence comparison remains a computational problem as the total number of sequences in the underlying databases grows exponentially with the progress of research[1]. Algorithms devised for the comparison of molecular sequences are based on the concept of string matching[2]. The newly proposed alignment-free sequence comparison algorithm is based on the concept of string matching. techniques. In Brute Force method, the string matching algorithm compares a pattern character by character in each and every location of the text. It is possible to solve the problems of strings matching with the help of finite automata[3]. Using finite automata, string matching automation is built from the pattern as a preprocessing step before matching. The text is then scanned through the automation to find occurrences of the pattern in the text. The Knuth-Morris-Pratt algorithm avoids back-tracking on the text when a mismatch occurs, by exploiting the knowledge of the matched substring in the text prior to the mismatch[4]. The main peculiarity of the Boyer-Moore algorithm is that some of the characters in the text can be skipped completely without comparing them with the pattern as it can be shown that they can never contribute to an occurrence of the pattern in the text[5]. In Logical Match, the sequence is arranged so that each element in the pattern are encoded as binary digits and coincides with it’s corresponding index and then proceed to
II METHOD
Phase - I i, Each characters are encoded as binary digits and generate the indices of Text and Pattern using Logical Match Phase - II ii, Compute number Mismatch(Text,Pattern)
of
Match(Text,Pattern)
iii, Compute score, S(Text,Pattrn) = Match in Text *µMatch(Pattern)[Pattern] – Mismatch in Text*µMismatch(Pattern)[Pattern] , where, µMatch(Pattern)[Pattern] + µMismatch(Pattern)[Pattern] = 1
( See Appendix )
and
III
Text => Pattern => a)
Encoded binary digits
Phase- I: Generating indices of Text and Pattern using Logical Match
Initialize {1000←A ,0100←T,0010←G,0001←C} Shift the text(Table 1) and pattern(Table 2) so that each encoded binary digit in the sequence coincides with it’s corresponding index in it’s respective column. Text => < 1000(1,4,6,7,10); 0100(3,9); 0010(5); 0001(2,8) > 0/1 10 9 8 7 6 5 4 3 2 1
1 0 0 1 1 0 1 0 0 1
0/1 0/1 0 0 1 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 Table 1. Text(Phase- 1)
0/1 0 0 1 0 0 0 0 0 1 0
Pattern => < 1000(1,7,9,10); 0100(3); 0010(5,6,8); 0001(2,4) >
10 9 8 7 6 5 4 3 2 1
b) Phase-II: Compute the number of match and mismatch using Logical Match(Table 3).
SIMULATION WITH ARTIFICIAL DATUM
0/1 0/1 0/1 1 0 0 0 0 0 0 0 1 1 0 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 Table 2. Pattern(Phase- 1)
Match/ Mismatch
Indices 9
10
1st Match
1000
1
7
0001
2
4
0100
3
1000
1
7
9
0010
5
6
8
1000
1
7
9
10
2nd Mismatch
1000
1
7
9
10
5th Match
0001
2
4
0100
3
1000
1
2nd Match 3rd Match 10
1st Mismatch 4th Match
3rd Mismatch 4th Mismatch
7
9
10
6th Match
Table 3. Alignment-free comparison using Logical Match Compute the score membership values. 0/1 0 1 0 1 0 0 1 0 1 0
using
automatically
generating
Score = = Match in Text *µMatch(Pattern)[Pattern] – Mismatch in Text * µMismatch(Pattern)[Pattern] = 6* 0.6 - 4* 0.4 = 3.6-1.6 = 2 IV EXPERIMENTAL RESULTS To simulate, alignment–free sequence comparison using Logical Match, the program has been written in C++ language under Linux platform. The method was tested against DNA sequences, the inputs have taken from the Locus ACU90045 as common text and ACU90045, PAU90054, HSU90049, LPU90051, NAU90053, DCU90047,
DPU90048 as patterns of common range 541-560 from NCBI
databank(Table 4). In the phase- I of the algorithm, the time complexity is O(m+n) and in the phase- II, the computational time depends on the lengths of the elements in the pattern of the text. V CONCLUSION We have presented the algorithm for alignment-free sequence comparison using Logical Match. The method provides a solution to find alignment- free similarities between two finite sequences by calculating the score using automatically generating fuzzy membership values. This procedure can possibly be implemented in the applications related to the alignment-free comparison of sequential patterns. Table 4 Locus
Region: 541-560(20bp)
Score Match(%)
T: ACU90045 cgacctctggacaggccact P ACU90045 cgacctctggacaggccact
20
100%
T: ACU90045 cgacctctggacaggccact P: PAU90054 cgacccactgagaaacctct
-2
45%
T: ACU90045 cgacctctggacaggccact P: HSU90049 cgaccaactgacaaggctct
-6
35%
T: ACU90045 cgacctctggacaggccact P: LPU90051 cgtcccactgacaagcctct
-8
30%
T: ACU90045 cgacctctggacaggccact P: NAU90053 cgcccaactgacaaggctct -10
25%
T: ACU90045 cgacctctggacaggccact P: DCU90047 aggcctttggacaaacctct -12
20%
T: ACU90045 cgacctctggacaggccact P: DPU90048 agaccagttgacaaaccttt -16
10%
[2] Gusfield D.(1997). Algorithms on Strings, Trees and Sequences: Computer Science and Computational Biology, Cambridge University Press. [3] Alfred V.Aho, Margaret J.Corasick.(1975). Efficient string matching: an aid to bibliographic search. Communications of the ACM. Volume 18, pp 333-340 [4] Knuth D.E, Morris (Jr) J.H., Pratt V.R.(1977). Fast pattern matching in strings, SIAM Journal on Computing 6(1), pp 323350. [5] Boyer R.S, Moore J.S.(1977). A fast string searching algorithm. Communications of the ACM. 20, pp 762-772. [6] Norwich A M and Turksen I B(1984). A model for the measurement of membership and the consequence of its empirical implementation .Fuzzy Sets and Systems 12, pp 1–25. [7] Dombi J.(1990). Membership function as an evaluation Fuzzy Sets and Systems 35, pp 1-21. [8] Medasani S, Kim J,Krishnapuram R.(1998). An Overview of membership function generation techniques for pattern recognition. International Journal of Approximate Reasoning 19, pp 391-471. [9] James C. Bezdek, James Keller, Raghu Krisnapuram, Nikhil R.Pal.(1999). Fuzzy Models and Algorithm for Pattern Recognition and Image Processing, Kluwer Academic Publishers. [10] www.ncbi.nlm.nih.gov
APPENDIX Let T and P be two strings of lengths n and m respectively, where n ≥ m. When P compares(alignment-free) with T gives r matches and s mismatches , r + s = m Match(P) [P] + Mismatch(P) [P] = Match in P/|P| + Mismatch in P/|P| = (Match in P + Mismatch in P)/|P|
Where, T and P are Text and Pattern respectively.
= (r + s) / m = m / m = 1 Example a)
ACKNOWLEDGMENT SSKP was funded in part by European Research and Educational Collaboration with Asia REFERENCES [1] Susana Vinga, Jonas Almeida.(2003). Alignment-free sequence comparison- a review. Bioinformatics.Vol.19, pp 513-523.
T => 0 1 0 1 0 0 1 0 | | | # # | # | P => 0 1 0 0 1 0 0 0 Match(Pattern) [P] = 5/8 = 0.625, Mismatch(Pattern) [P] = 3/8 = 0.375 Score(T ,P) = Match in T *µMatch(P)[P] –
Mismatch in T*µMismatch(P)[P]
= 5*0.625 - 3* 0.375 = 3.125 - 1.125 = 2
Example c)
Example b) T => 0 1 0 1 0 0 1 0 | | | # # | # # P => 0 1 0 0 1 0 0 -Match(Pattern) [P] = 4/7 = 0.571 Mismatch(Pattern) [P] = 3/7 = 0.428 Score(T ,P) = Match in T *µMatch(P)[P] –
Mismatch in T*µMismatch(P)[P] = 4*0.571 - 4* 0.428 = 2.284 - 1.712 = 0.572
T => 0 1 0 1 0 0 1 0 | | | # # # # # P => 0 1 0 0 -- -- -- -Match(Pattern) [P] = 3/4 = 0.75, Mismatch(Pattern) [P] = 1/4 = 0.25 Score(T ,P) = Match in T *µMatch(P)[P] –
Mismatch in T*µMismatch(P)[P] = 3*0.75 - 5* 0.25 = 2.25 - 1.25 =1
